_Loop Cut_ will only work with quads, i.e. faces consisting of 4 edges and vertices. When you choose an edge where you want to start the loop cut, it continues over the opposite edge. This means a loop cut cannot be performed if the face has more or less than 4 edges because there is no distinct opposite face.

What you can do in _Edit Mode_ is go into _Front Orthographic_ view by pressing <kbd>Numpad 1</kbd>, then <kbd>K</kbd> for the _Knife Tool_, press <kbd>C</kbd> for _angle constraint_ > _ON_ and to make sure everything will be cut also press <kbd>Z</kbd> for _cut through_ > _ON_.

Now move the knife to the top edge until a green square appears, left-click, go down to the bottom edge (the _angle constraint_ option provides a straight vertical cut) until another green square appears and left-click again.

To confirm the single cut now press <kbd>Return</kbd>. Or instead, to prepare more cuts at once press <kbd>E</kbd>, then repeat the left-clicking like before on a different region of the edges. After you've selected all cuts hit <kbd>Return</kbd> to confirm.